Related papers: Advances in finding ideal play on poset games

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…

Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…

In this paper, we consider a game beginning with a multiset of elements from a group. On a move, two elements are replaced by their sum. This is a no strategy game, and can be modeled as a graded poset with the rank of a node equal to the…

Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective…

Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…

The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms…

Stochastic games are a classical model in game theory in which two opponents interact and the environment changes in response to the players' behavior. The central solution concepts for these games are the discounted values and the value,…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…

We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction…

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…

Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…

We study the problem of finding equilibrium strategies in multi-agent games with incomplete payoff information, where the payoff matrices are only known to the players up to some bounded uncertainty sets. In such games, an ex-post…

This article concerns the resolution of impartial combinatorial games, and in particular games that can be split in sums of independent positions. We prove that in order to compute the outcome of a sum of independent positions, it is always…

This paper introduces alignment games, a new class of zero-sum games modeling strategic interventions where effectiveness depends on alignment with an underlying hidden state. Motivated by operational problems in medical diagnostics,…

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…